Page 150 - Mechanical design of microresonators _ modeling and applications

0-07-145538-8_CH03_149_08/30/05

Microhinges and Microcantilevers: Lumped-Parameter Modeling and Design

Microhinges and Microcantilevers: Lumped-Parameter Modeling and Design 149
α

w 2 1 2
w1

1 1
Figure 3.28 Top view of a hollow trapezoid microcantilever.

The axial resonant frequency is

Ew 1
Ȧ =2.45 (3.123)
a,e ȡl (2l w +3l w )cos Į
1 1 1 2 2
The torsional stiffness is
2EGw t 3
1
k t,e = (3.124)
2
2
3l (E cos Į +4G sin Į )
1
The torsional resonant frequency is
EGw 1
Ȧ =4.9t
t,e 2 2 2 2 2
ȡl 2l w (w + t ) +3l w (w + t ) (E cos Į (3.125)
1 1 1 1 2 2 2
2
+4G sin Į)
The bending stiffness is

3
8EGw t
1
k b,e = (3.126)
l { 16Gl +3l El cos Į +4G(2l + l sin Į )sin Į }
2
2
1 1 2 2 1 2
The bending resonant frequency is
EGtw
Ȧ =2.83t 1
b,e 2
1 1/
ȡtl (33l w 70 + l w ){16Gl
1 2 2 1 (3.127)
+3l El cos Į +4G(2l + l sin Į )sin Į }
2
2 2 1 2

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